Matthew J. Vavrek

Tooth counts through growth in diapsid reptiles: implications for interpreting individual and size-related variation in the fossil record

Tooth counts are commonly recorded in fossil diapsid reptiles and have been used for taxonomic and phylogenetic purposes under the assumption that differences in the number of teeth are largely explained by interspecific variation. Although phylogeny is almost certainly one of the greatest factors influencing tooth count, the relative role of intraspecific variation is difficult, and often impossible, to test in the fossil record given the sample sizes available to palaeontologists and, as such, is best investigated using extant models. Intraspecific variation (largely manifested as size‐related or ontogenetic variation) in tooth counts has been examined in extant squamates (lizards and snakes) but is poorly understood in archosaurs (crocodylians and dinosaurs). Here, we document tooth count variation in two species of extant crocodylians (Alligator mississippiensis and Crocodylus porosus) as well as a large varanid lizard (Varanus komodoensis). We test the hypothesis that variation in tooth count is driven primarily by growth and thus predict significant correlations between tooth count and size, as well as differences in the frequency of deviation from the modal tooth count in the premaxilla, maxilla, and dentary. In addition to tooth counts, we also document tooth allometry in each species and compare these results with tooth count change through growth. Results reveal no correlation of tooth count with size in any element of any species examined here, with the exception of the premaxilla of C. porosus, which shows the loss of one tooth position. Based on the taxa examined here, we reject the hypothesis, as it is evident that variation in tooth count is not always significantly correlated with growth. However, growth trajectories of smaller reptilian taxa show increases in tooth counts and, although current samples are small, suggest potential correlates between tooth count trajectories and adult size. Nevertheless, interspecific variation in growth patterns underscores the importance of considering and understanding growth when constructing taxonomic and phylogenetic characters, in particular for fossil taxa where ontogenetic patterns are difficult to reconstruct.

Small sample sizes in the study of ontogenetic allometry; implications for palaeobiology

Quantitative morphometric analyses, particularly ontogenetic allometry, are common methods used in quantifying shape, and changes therein, in both extinct and extant organisms. Due to incompleteness and the potential for restricted sample sizes in the fossil record, palaeobiological analyses of allometry may encounter higher rates of error. Differences in sample size between fossil and extant studies and any resulting effects on allometric analyses have not been thoroughly investigated, and a logical lower threshold to sample size is not clear. Here we show that studies based on fossil datasets have smaller sample sizes than those based on extant taxa. A similar pattern between vertebrates and invertebrates indicates this is not a problem unique to either group, but common to both. We investigate the relationship between sample size, ontogenetic allometric relationship and statistical power using an empirical dataset of skull measurements of modern Alligator mississippiensis. Across a variety of subsampling techniques, used to simulate different taphonomic and/or sampling effects, smaller sample sizes gave less reliable and more variable results, often with the result that allometric relationships will go undetected due to Type II error (failure to reject the null hypothesis). This may result in a false impression of fewer instances of positive/negative allometric growth in fossils compared to living organisms. These limitations are not restricted to fossil data and are equally applicable to allometric analyses of rare extant taxa. No mathematically derived minimum sample size for ontogenetic allometric studies is found; rather results of isometry (but not necessarily allometry) should not be viewed with confidence at small sample sizes.

Ecological modelling, size distributions and taphonomic size bias in dinosaur faunas: a comment on Codron et al. (2012).

Codron et al. [[1][1]] invoke an ecological model of size-specific competition in dinosaurs to explain an apparent bimodal distribution within Dinosauria, and find ‘intermediate-sized taxa’ (1–1000 kg) are prone to extinction. Although the authors take an interesting approach, we argue that

A comparison of clustering methods for biogeography with fossil datasets

Cluster analysis is one of the most commonly used methods in palaeoecological studies, particularly in studies investigating biogeographic patterns. Although a number of different clustering methods are widely used, the approach and underlying assumptions of many of these methods are quite different. For example, methods may be hierarchical or non-hierarchical in their approaches, and may use Euclidean distance or non-Euclidean indices to cluster the data. In order to assess the effectiveness of the different clustering methods as compared to one another, a simulation was designed that could assess each method over a range of both cluster distinctiveness and sampling intensity. Additionally, a non-hierarchical, non-Euclidean, iterative clustering method implemented in the R Statistical Language is described. This method, Non-Euclidean Relational Clustering (NERC), creates distinct clusters by dividing the data set in order to maximize the average similarity within each cluster, identifying clusters in which each data point is on average more similar to those within its own group than to those in any other group. While all the methods performed well with clearly differentiated and well-sampled datasets, when data are less than ideal the linkage methods perform poorly compared to non-Euclidean based k-means and the NERC method. Based on this analysis, Unweighted Pair Group Method with Arithmetic Mean and neighbor joining methods are less reliable with incomplete datasets like those found in palaeobiological analyses, and the k-means and NERC methods should be used in their place.

Pachycephalosaurid (Dinosauria: Ornithischia) cranial remains from the latest Cretaceous (Maastrichtian) Scollard Formation of Alberta, Canada

Maastrichtian terrestrial deposits throughout Laramidia (western North America) have yielded a wealth of ancient dinosaur diversity. Yet, despite intense collecting in some areas, latitudinal sampling unevenness still limits biogeographic studies, making new records of dinosaur occurrences significant. Here, we describe the first non-dental pachycephalosaurid cranial material from the late Maastrichtian Scollard Formation of central Alberta, Canada, which allows more precise taxonomic identification of pachycephalosaurids from the northern part of the Western Interior Basin during this time interval. A domed parietal, although weathered, retains several features that allow it to be referred to the tribe Pachycephalosaurini within the subfamily Pachycephalosaurinae, and likely to the genus Pachycephalosaurus. This specimen provides further support for the suggestion that late Maastrichtian dinosaur communities were generally cosmopolitan with no discrete faunal provinces in Laramidia, and underscores the importance of collecting fragmentary, but identifiable remains that often go unreported.

The fragmentation of Pangaea and Mesozoic terrestrial vertebrate biodiversity.

During the Mesozoic (242–66 million years ago), terrestrial regions underwent a massive shift in their size, position and connectivity. At the beginning of the era, the land masses were joined into a single supercontinent called Pangaea. However, by the end of the Mesozoic, terrestrial regions had become highly fragmented, both owing to the drifting apart of the continental plates and the extremely high sea levels that flooded and divided many regions. How terrestrial biodiversity was affected by this fragmentation and large-scale flooding of the Earths landmasses is uncertain. Based on a model using the species–area relationship (SAR), terrestrial vertebrate biodiversity would be expected to nearly double through the Mesozoic owing to continental fragmentation, despite a decrease of 24% in total terrestrial area. Previous studies of Mesozoic vertebrates have generally found increases in terrestrial diversity towards the end of the era, although these increases are often attributed to intrinsic or climatic factors. Instead, continental fragmentation over this time may largely explain any observed increase in terrestrial biodiversity. This study demonstrates the importance that non-intrinsic effects can have on the taxonomic success of a group, and the importance of geography to understanding past biodiversity.

Xiphactinus audax Leidy 1870 from the Puskwaskau Formation (Santonian to Campanian) of northwestern Alberta, Canada and the distribution of Xiphactinus in North America

Xiphactinus is one of the largest teleost fish known from the Late Cretaceous of North America, and has been found across much of the Western Interior Basin. Despite extensive Late Cretaceous marine deposits occurring in Alberta, there has previously been only two possible records of Xiphactinus from the province, neither of which has been diagnosable to the species level. We describe here a portion of the lower jaws, including teeth, of Xiphactinus audax from northeast of Grande Prairie, Alberta. The fossil has large, thecodont teeth that are circular in cross section and lack any carinae, and are highly variable in their overall size. This fossil is the first diagnostic material of X . a udax from Alberta, and extends the range of the species by over a thousand kilometres. During the Late Cretaceous, the area the fossil was found in was near the Arctic Circle, and represents an important datapoint within the poorly known, northern portion of the Western Interior Basin.